Math Is Fun Forum

They sent me two e-mails, none of which mentions the prize I've won.

It's nice to have so many free books today. Thank you Ricky.

I just corrected my watch! Yaahoo!

First, I would suggest you to solve x out using the identity VQ=VW+WQ
Then, you can draw RB vertical to TU and PS with intersection A and B. I think you can work it out now.

Okay, I admit I have a causality preassumption in my mind.
I don't believe:
A change could happen out of the constant.

I believe it should have been caused, either externally or internally.

Game theory.
I would rather see the game as a mimic of two competing firms at the point to decide whether or not to invest in R&D unprotected. And this makes it less cruel.

You don't have to
You can point out A'A= (A'A)'
and (A'A)[sup]-1[/sup]= [(A'A)[sup]-1[/sup]]',
which  need each theorems to prove.
In addition, there is no way to eliminate (A' A)^(-1) generally, and the final formula involves it.

I have one way to figure them out without a calculator. But you need other tools.
Find a piece of hard-paper, draw a circle with radius of integer centimetres, and cut. Also depict the co-ords cross with pen. Next time you wanna figure out a sin, just measure it from the round paper you carry with an angle-measure and a ruler. Sure you can improve the special tool, too. You can paste co-ords paper onto it so you may not need a ruler, and you can draw 10°, 20°,... on to it so that you no longer need to carry the tool to measure the angle if you are not that exact about the result.

Great point, since you finally keep it in mind. I'll explore the other paradoxes soon. Wait for me

as categorily distributed as in the population.
For example, male:female=100:105
kids:whole=1/10 or something.
And, sufficiantly large sample, better at least 35 for each category, so your overall data might contain hundreds of samples.

Nice challenge.
Typically they would argue
0.1/0.1=1
0.01/0.01=1
0.001/0.001=1
......
Hence 0/0 could be defined as 1 when in the function x/x.

But I find this reason tricky and would refuse it.

most of whom aren't experts in statistics and none of whom have probably have read the papers you're referring to.
-he he, you are right.

However, this time I have been patient, and I think s-c you probably made the problem too complicated.

First, forget about birthday and life-span. Let's say a person could die at any date of any year. And generally, he/she has the same chance, or almost the same chance to die on some Jan 1st , some July 1st or some Dec 31st. In the same year the date may represent some different life-spans, but they may represent another different ones in different years.

Hence the problem could be simplier. Count how many significant days in a year, and how-many/365.25 would be the general frequency of significant days across the history, then mutiply each relative's how-many/365.25 to represent they all die on some significant day.